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Nonclassical interpolation in spaces of smooth functions

Vladimir Ovchinnikov — 1999

Studia Mathematica

We prove that the fractional BMO space on a one-dimensional manifold is an interpolation space between C and $C^{1}$ . We also prove that $B M O^{1}$ is an interpolation space between C and $C^{2}$ . The proof is based on some nonclassical interpolation constructions. The results obtained cannot be transferred to spaces of functions defined on manifolds of higher dimension. The interpolation description of fractional BMO spaces is used at the end of the paper for the proof of the boundedness of commutators of the Hilbert...

On the relation between complex and real methods of interpolation

Mieczysław Mastyło; Vladimir Ovchinnikov — 1997

Studia Mathematica

We study those compatible couples of Banach spaces for which the complex method interpolation spaces are also described by the K-method of interpolation. As an application we present counter-examples to Cwikel's conjecture that all interpolation spaces of a Banach couple are described by the K-method whenever all complex interpolation spaces have this property.

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